1. Measures of Effectiveness 1 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Chapter 7 Demand Forecasting in a Supply Chain Forecasting - 3 Demand Pooling Ardavan Asef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs, Chase, and Aquilano Supply Chain Management: Chopra and Meindl

2. Measures of Effectiveness 2 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Operations Management Session 16: Trend and Seasonality

3. Measures of Effectiveness 3 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Previous Lecture  The importance of forecasting?  Forecast  Forecast is not a single number  Error measure MAD  Moving average  Exponential smoothing  Tradeoff: stability and responsiveness  Static Model for trend and Seasonality

4. Measures of Effectiveness 4 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Today’s Lecture  An application of the exponential smoothing method  Risk-pooling effect again!  Trend forecast  Seasonal forecast

5. Measures of Effectiveness 5 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions: How many to stock? A firm produces Red and Blue T-Shirts

6. Measures of Effectiveness 6 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions (  = 0.3) MonthT-Shirt DemandForecast January909.9 February616.7909.9 March1073.3821.94 April1382.9897.348 May1359.51043.014 June1519.91137.96 July344.91252.542 August929.7980.2492 September1328.5965.0844 October6741074.109 November954.0764

7. Measures of Effectiveness 7 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions  Suppose the company stocks 954 T-shirts, the forecasted number. What is the probability the company will have a stockout, that is, that there will not be enough T-shirts to satisfy demand?  The company does not want to have unsatisfied demand, as that would be lost revenue. So the company overstocks. Suppose the company stocks 1,026 units.  What is the probability that the actual demand will be larger than 1,026?

8. Measures of Effectiveness 8 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 There is a Distribution Around the Forecasted Sale Standard Deviation of Error = 1.25 MAD  Error is assumed to NORMALLY DISTRIBUTED with A MEAN (AVERAGE) = 0 STANDARD DEVIATION = 1.25* MAD

9. Measures of Effectiveness 9 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecasts and Probability Distributions (  = 0.3) MonthT-Shirt DemandForecastAD January909.9 February616.7909.9293.2 March1073.3821.94251.36 April1382.9897.348485.552 May1359.51043.014316.4864 June1519.91137.96381.9405 July344.91252.542907.6417 August929.7980.249250.54916 September1328.5965.0844363.4156 October6741074.109400.1091 November954.0764

10. Measures of Effectiveness 10 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 How many to stock Suppose the company desires that the probability of not being able to meet demand is 2.5% Look-up on normal table (show using book)

11. Measures of Effectiveness 11 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 How many to stock Note that MAD=383 in this example.

12. Measures of Effectiveness 12 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 The Forecast for a Blue Products (  = 0.3)

13. Measures of Effectiveness 13 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Blue Product Inventory Level  The stocking level, of the blue product, for period 11 is: 1148+1.96*(1.25*237)=1728  Recall that: amt. stocked = forecast + 1.96x1.25xMAD implies the probability of not satisfying demand is P( demand > amt. stocked ) = 0.025.

14. Measures of Effectiveness 14 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Total Inventory Level  The total inventory for Red and Blue is: 1892 + 1728 = 3620  P( Red demand > # of Red T-shirts stocked ) = 0.025 P( Blue demand > # of Blue T-shirts stocked ) = 0.025

15. Measures of Effectiveness 15 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Aggregate Forecasts  Can we more accurately forecast the combined demand?  Suppose we can make Gray Shirt and then dye the T-shirts either red or blue.  What is the Demand for Gray Shirts?  We look at the sum of the demands in the past  We forecast the demand for the two products combined  We compute the MAD for the aggregate forecast

16. Measures of Effectiveness 16 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Forecast for the Aggregate Demand Inventory of Gray = 2102 + 1.96*1.25*614 = 3603

17. Measures of Effectiveness 17 Ardavan Asef-Vaziri 6/4/2009 Forecasting - 4 Aggregate Demand Forecast Conclusions  By stocking 3603 Gray T-shirts, we ensure P( T-shirt demand > # stocked ) = 0.025  Otherwise, we needed to stock 1892 blue T-shirts and 1728 red T-shirts for a combined number of 1892+1728 = 3620 T-shirts to ensure that P( red T-shirt demand > # red shirts stocked) = P( blue T-shirt demand > # blue shirts stocked) = 0.025  3603 < 3620 … we need to stock less T-shirts to ensure a given stockout probability (2.5% in this example) when we have an aggregate forecast.